Many people are afraid of sharks, or perhaps more accurately the idea of sharks. What I've seen happen with divers that feel this way, is once they are lucky enough to see one in the water, they quickly realize what everyone said is true - the shark could care less about them and is mostly either ignoring them or swimming away. Next thing you know they're trying to get a better look and the fear thing goes right out the window. Just respect them and educate yourself - a good idea for all the critters. (Don't do something silly like pull the tail of a nurse shark because they seem so harmless - I know someone who did this, an avid but clueless snorkeler.)
Of course you can go on special shark feeding dives or to locations that are very sharkey, and then you'll see more sharks closer that may hang around longer. But you have to make a point of doing this, and the sharks still don't care about you or anything other than the food or whatever brings them to that spot.
You've gotten a lot of the typical answers you should get, but not all of the answers you need.
The idea that you'll be lucky to ever see a shark, that they are like puppies... well.... that really all depends on how much diving you end up doing and how far flung it is on this planet. Like driving a car, you can drive to work and to and fro the mall and take the kids to soccer for years and years and never have a problem, but that doesn't mean someday you can't be broadsided by a drunk driver.
This is the same with sharks. For the most part, most species of sharks are more scared of you then you are of them and you'll never really get very close. However, that doesn't mean you can't eventually have an encounter very different than what 99% of encounters are typically like. The more diving you do, the more variety of locations you dive, the odds are going up that your encounter might change.
There are more elements than just the average shark and the average environment that can effect an encounter. One of the single most influential things that effect how sharks will interact with humans is how humans have been interacting with them and that is through changing their behavior through feeding. When shark feeding goes on it changes sharks dramatically. Another influence is spear fishing. Both of these can dramatically change shark behavior from boring sharks that stay far away from you, that you're lucky to get a good look at them, to sharks that come right up to you eye ball to eye ball to check you out, bump you and more. I've personally batted sharks away from me who were obviously fed and now associate humans with food and get very aggressive and curious. I've also dived waters as close and as mundane as the waters of Jupiter Florida where sharks when they hear a spear gun go off will b-line it to that area, checking out every diver they home in on to see if they have a catch that they can try to steal, those encounters will not be the typical shark at 30 feet keeping it's distance from you, those encounters can be a shark within 12-18 inches of you, big and in your face.
I've never been bitten by any sharks on any encounters but I've certainly had sharks way too close to my personal space to the point of them making me nervous and not liking it as they are big powerful animals that can change your life in an instant.
So while nobody wants to get your more nervous about sharks, I will be honest with you and let you know the puppy dog encounters many people associate with sharks isn't always going to be the case. Just like being hit by a drunk driver, the more driving (diving) you do in the more places the higher the chances of having an encounter out of the norm. The norm should be that sharks keep their distance from you, that doesn't mean this can't change because it certainly can. Keep in mind we aren't talking about a shark attacking or biting you, just that your encounter may not be totally boring.
